This invention relates to improvements in the apparatus disclosed in U.S. Pat. No. 4,884,785 which issued to the assignee of the present invention, and the disclosure of which is herein incorporated by reference. The apparatus is used with a tire lift/carrier unit or hoist of the type disclosed in U.S. Pat. No. 5,290,014 which also issued to the assignee of the present invention and the disclosure of which is hereby incorporated by reference. In such apparatus, it is desirable to minimize lateral movement of the stored spare tire and wheel assembly in the event of a sudden shock or impact to the motor vehicle. It is also desirable to provide a secondary support mechanism or apparatus which is simple and dependable in construction and operation and which provides for moving the support bracket for the spare tire and wheel assembly between its retracted and extended positions when the assembly has been removed for use or repair. Also, in the event the lift unit fails or the cable breaks, and the secondary support system or mechanism becomes effective to support the tire and wheel assembly in an elevated position, it is desirable to provide for conveniently releasing the spare tire and wheel assembly for lowering and removing the assembly from the vehicle.